Noncompactness and noncompleteness in isometries of Lipschitz spaces
Jesús Araujo,Luis Dubarbie +1 more
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In particular, this article showed that requirements of completeness on X and Y are not necessary when E and F are not complete, which is in sharp contrast with results known in the scalar context.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 2011-05-01 and is currently open access. It has received 20 citations till now. The article focuses on the topics: Uniform continuity & Isometry.read more
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Extreme points and isometries on vector-valued Lipschitz spaces
TL;DR: In this paper, the authors investigate the nature of the extreme points of the dual ball for the embedding of a continuous vector-valued Lipschitz function into a compact set and use the information to describe the surjective isometries on Lip (X, E ) under certain conditions on E, where E is not assumed to be strictly convex.
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Compact composition operators on noncompact Lipschitz spaces
TL;DR: In this paper, the authors characterize compact composition operators between different spaces of scalar-valued Lipschitz functions defined on metric spaces, not necessarily compact, and determine their spectra.
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2-Local standard isometries on vector-valued Lipschitz function spaces
TL;DR: In this paper, the authors give a description of the 2-local (standard) isometries on the Banach space Lip ( X, E ) of vector-valued Lipschitz functions from X to E in terms of a generalized composition operator.
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2-local standard isometries on vector-valued Lipschitz function spaces
TL;DR: In this article, the authors give a description of the standard isometries on the Banach space of vector-valued Lipschitz functions from a compact metric space to a Banach metric space.
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Isometries on spaces of absolutely continuous vector-valued functions
TL;DR: In this article, the surjective (not necessarily linear) isometries between spaces of absolutely continuous vector-valued functions with respect to the norm of the supremum norm were investigated.
References
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Book
Introductory functional analysis with applications
TL;DR: In this paper, the spectral theory of linear operators in normed spaces and their spectrum has been studied in the context of bounded self-and-adjoint linear operators and their applications in quantum mechanics.
Book
Isometries on Banach Spaces: function spaces
Richard J. Fleming,James Jamison +1 more
TL;DR: Banach's characterisation of isometries on C(Q) and C(p) spaces is described in this article, along with a discussion of the different types of spaces in the BANACK-STONE THEOREM.
Book
M-Structure and the Banach-Stone Theorem
TL;DR: In this paper, the Banach-Stone theorem is generalized to Co(M,X) and the centralizer-norming system is proposed. But the centralization is not considered in this paper.
Journal ArticleDOI
The Space of Bounded Maps into a Banach Space
TL;DR: In this article, the authors extend the results of this theory to the space Bx of bounded continuous maps from the topological space X into the real Banach space B. The result is obtained, however, with certain restrictions on B, and for such a space an explicit formula is given for the relation between an equivalence of Bx and BY and a homeomorphism of X and Y (?6).